Infinitely many solutions for boundary value problems arising from the fractional advection dispersion equation

Jing Chen; Xian Hua Tang

Applications of Mathematics (2015)

  • Volume: 60, Issue: 6, page 703-724
  • ISSN: 0862-7940

Abstract

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We consider the existence of infinitely many solutions to the boundary value problem d d t 1 2 0 D t - β ( u ' ( t ) ) + 1 2 t D T - β ( u ' ( t ) ) + ∇ F ( t , u ( t ) ) = 0 a.e. t ∈ [ 0 , T ] , u ( 0 ) = u ( T ) = 0 . Under more general assumptions on the nonlinearity, we obtain new criteria to guarantee that this boundary value problem has infinitely many solutions in the superquadratic, subquadratic and asymptotically quadratic cases by using the critical point theory.

How to cite

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Chen, Jing, and Tang, Xian Hua. "Infinitely many solutions for boundary value problems arising from the fractional advection dispersion equation." Applications of Mathematics 60.6 (2015): 703-724. <http://eudml.org/doc/271820>.

@article{Chen2015,
abstract = {We consider the existence of infinitely many solutions to the boundary value problem \begin\{gather\} \frac\{\{\rm d\}\}\{\{\rm d\} t\}\Big (\frac\{1\}\{2\} \_\{0\}D\_\{t\}^\{-\beta \}(u^\{\prime \}(t)) +\frac\{1\}\{2\} \_\{t\}D\_\{T\}^\{-\beta \}(u^\{\prime \}(t))\Big )+\nabla F(t,u(t))=0 \quad \text\{\rm a.e.\}\ t\in [0,T],\nonumber \\ u(0)=u(T)=0.\nonumber \end\{gather\} Under more general assumptions on the nonlinearity, we obtain new criteria to guarantee that this boundary value problem has infinitely many solutions in the superquadratic, subquadratic and asymptotically quadratic cases by using the critical point theory.},
author = {Chen, Jing, Tang, Xian Hua},
journal = {Applications of Mathematics},
keywords = {fractional boundary value problem; critical point theory; variational methods; fractional boundary value problem; critical point theory; variational methods},
language = {eng},
number = {6},
pages = {703-724},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Infinitely many solutions for boundary value problems arising from the fractional advection dispersion equation},
url = {http://eudml.org/doc/271820},
volume = {60},
year = {2015},
}

TY - JOUR
AU - Chen, Jing
AU - Tang, Xian Hua
TI - Infinitely many solutions for boundary value problems arising from the fractional advection dispersion equation
JO - Applications of Mathematics
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 6
SP - 703
EP - 724
AB - We consider the existence of infinitely many solutions to the boundary value problem \begin{gather} \frac{{\rm d}}{{\rm d} t}\Big (\frac{1}{2} _{0}D_{t}^{-\beta }(u^{\prime }(t)) +\frac{1}{2} _{t}D_{T}^{-\beta }(u^{\prime }(t))\Big )+\nabla F(t,u(t))=0 \quad \text{\rm a.e.}\ t\in [0,T],\nonumber \\ u(0)=u(T)=0.\nonumber \end{gather} Under more general assumptions on the nonlinearity, we obtain new criteria to guarantee that this boundary value problem has infinitely many solutions in the superquadratic, subquadratic and asymptotically quadratic cases by using the critical point theory.
LA - eng
KW - fractional boundary value problem; critical point theory; variational methods; fractional boundary value problem; critical point theory; variational methods
UR - http://eudml.org/doc/271820
ER -

References

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